Abstract : We investigate various characterizations of the Haagerup property H for a second countable locally compact group G, in terms of orthogonal representations of G on non-commutative Lp spaces. We introduce a variant H Lp for orthogonal representations with vanishing coefficients on Lp, and study its relationships with property H. We also give a characterization of H by the means of strongly mixing actions on a non-commutative Lp space. We construct proper actions of groups with H by affine isometries on some non-commutative Lp space, such as the Lp space associated to the hyperfinite II infinite factor.